example1

• A batter’s average number of hits per baseball season can be modelled using the normal distribution with a mean of 0.295 hits and a standard deviation of 0.10 hits. Sketch this normal distribution. How does the graph change if the standard deviation decreases to 0.04? How does the graph change if the mean increase to 0.399?

example2

• The heights of 16-month-old maple seedlings are normally distributed with a mean of 30 cm and a standard deviation of 14.1 cm. What is the probability that the height of a randomly selected seedling will be between 25.0 cm and 39.0 cm?

example3

• Determine the area under the standard normal curve that lies to the left of z = 2.01.

example4

• Determine the area under the standard normal curve between z = 0.88 and z = 1.84.

example5

• Plot 500 observations from a normal distribution with a mean of 10 and standard deviation of 6. Calculate measures of center (mean, median and mode) and measures of spread (range, interquartile range, variance and standard deviation) for the sample.

example6

• Generate a sample of size 1000 from a standard normal distribution. Represent the sample with a frequency histogram and frequency polygon using different sizes of intervals. Compare the effectiveness of the frequency polygon as an approximation of the distribution as the number of intervals increase.